Search NASA⌕ Search

SEARCH · Search NASA

Results for “large deformations”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 559 records · Page 31

Impact of dark matter on tidal signatures in neutron star mergers with the Einstein Telescope

If dark matter (DM) accumulates inside neutron stars (NS), it changes their internal structure and causes a shift of the tidal deformability from the value predicted by the dense-matter equation of state (EOS). In principle, this shift could be observable in the gravitational-wave (GW) signal of binary neutron star (BNS) mergers. We investigate the effect of fermionic, noninteracting DM when observing a large number of GW events from DM-admixed BNSs with the precision of the proposed Einstein telescope (ET). Specifically, we study the impact on the recovery of the baryonic EOS and whether DM properties can be constrained. For this purpose, we create event catalogs of BNS mock events with DM fraction up to 1%, from which we reconstruct the posterior uncertainties with the Fisher matrix approach. Using this data, we perform joint Bayesian inference on the baryonic EOS, DM particle mass, and DM particle fraction in each event. Here, our results reveal that when falsely ignoring DM effects, the EOS posterior is biased toward softer EOSs, though the offset is rather small. Further, we find that within our assumptions of our DM model and population, ET will likely not be able to test the presence of DM in BNSs, even when combining many events and adding Cosmic Explorer (CE) to the next-generation detector network. Likewise, the potential constraints on the DM particle mass will remain weak because of degeneracies with the fraction and EOS.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

The 10 September 2025 M w 4.1 Earthquake in Northeastern Utah, United States: An Archetypal Continental Mantle Event

The 10 September 2025 M w 4.1 earthquake in northeastern Utah, United States, had a focal depth 68 km beneath sea level, which is ∼20–25 km greater than estimates of local crustal thickness, making it a rare example of a continental mantle earthquake (CME). The focal depth is well resolved from arrival-time inversion (nearest station ∼13 km away) and moment tensor inversion of regional waveforms. Similar to other CMEs in the Intermountain West, there were no obvious aftershocks or foreshocks, and the waveforms were enriched in high-frequency energy. Spectral modeling gives a stress drop of ∼80 MPa and a radiation efficiency of ∼0.08, albeit with large uncertainties. The high stress drop and low radiation efficiency are consistent with a dissipative source process such as thermal runaway. Also similar to previous Intermountain West CMEs, the event occurred along the boundary of the Archean Wyoming craton, where pressure–temperature conditions favor ductile deformation. We hypothesize that edge-driven or regional-scale mantle convection produces increased strain rates near the craton boundary that make either conventional brittle failure or thermal runaway feasible at relatively high pressure–temperature conditions. High conductivity inferred around the edge of the craton may suggest that fluids also contribute to CME occurrence.

Koper, Keith D. [Univ. of Utah, Salt Lake City, UT↗

Upcycling of Mixed Aluminum Alloy Shredder Scrap using Shear Processing

Conservation of critical materials is an increasing area of focus in the Unites States. In 2023, aluminum was added to the US Department of Energy Final Critical Materials List which has spurred public and private research into sustainable management of these resources. Additionally, efficiency in manufacturing and conservation of natural resources are growing concerns with targets to lower global carbon emissions, as primary aluminum alloy production is energy intensive, requiring 14 MWh of electricity plus 0.4 tonnes of CO2 per tonne of Al. Due to these factors, is essential that more sustainable manufacturing methods for aluminum alloys are developed going forward. To this end, much research is ongoing on the topic of more efficient utilization and recovery. However, most of this research still requires primary aluminum in the production process. Here, it will be attempted to bypass the use of primary aluminum and produce useful material recycled from 100% post-consumer scrap. Even considering recent developments in recycling of Al scrap, there is still a large amount of post-consumer scrap that is underutilized due to high impurity content, and that amount will increase significantly as more and more aluminum alloys are utilized in vehicles. This “scrap wave” is expected to cover 80% of the demand for automotive aluminum alloys by 2050 . A challenge to be addressed before the coming scrap wave can be fully utilized is that the tolerance of manufacturing techniques to impurities or off-spec alloy compositions must be increased. Particularly, in 5000-and 6000-series alloys (the most common wrought alloys in durable products), excess iron, copper, and silicon create brittle intermetallics during casting that remain in the extruded microstructure which limit the formability, ductility, and corrosion resistance of the alloy. Concerningly, many of the highest-volume post-consumer aluminum scrap streams such as automotive shredder scrap contain a mix of alloys including both wrought and cast alloys. Their compositions can vary widely depending on geography and the time of year. Because they are mixed, they often contain high content of multiple alloying elements such as Si and Cu in higher concentrations than are found in typical wrought alloys. They may also be contaminated with non-Al alloys from fasteners that get mixed in and often have high content of unwanted elements such as Fe. As a method for utilizing these underused scrap streams that are high in tramp elements, an emerging extrusion technology is being developed at the Pacific Northwest National Laboratory (PNNL) that aims to upcycle 100% post-consumer aluminum scrap directly into extruded components without the addition of primary aluminum . This new technology, called Shear Assisted Processing and Extrusion (ShAPE), is enabling a shift away from today’s recycling paradigm by reaching deeper into lower-value scrap streams, using shredder scrap as the extrusion billet material. Sometimes referred to as Twitch or Tweak, these scrap streams result from shredding and sorting of automobiles, building materials, appliances, and consumer goods. ShAPE combines the linear axis of conventional extrusion with a rotating extrusion die. This rotating die applies large strain to the material during extrusion, which breaks up large impurity-containing intermetallic particles, reducing their deleterious effects. This has been demonstrated for 6063 machining scrap spiked with excess Fe, and Twitch scrap high in Fe, Si and Cu where strength and ductility were retained for both feedstock compositions. Additionally, the extreme plastic deformation during ShAPE enables extrusion of billets with high Si that are too brittle for processing by conventional extrusion. By using 100% post-consumer shedder scrap as feedstock, ShAPE has the potential to slash embodied energy and carbon in extruded components by >80% compared to conventional extrusion of primary aluminum alloys.

Milligan, Brian K.↗

Instability of Nagaoka State and Quantum Phase Transition via Kinetic Frustration Control

We investigate the Nagaoka-Thouless (NT) ferromagnetic instability in the strongly interacting t-t' Hubbard model by continuously breaking particle-hole symmetry on a tunable square-triangular lattice geometry. We use an analytic approach to show that the fully spin-polarized state becomes unstable to a metastable spin-polaron when the kinetic frustration t'/t exceeds a critical, dimension-dependent value. Large-scale density matrix renormalization group (DMRG) simulations reveal a quantum phase transition from the NT ferromagnet to a spiral spin-density wave, which evolves continuously into the Haerter-Shastry antiferromagnet in the large-frustration limit. Remarkably, this transition remains robust at low but finite hole density, making it accessible in cold-atom and moiré Hubbard platforms under strong interactions. A variational analysis further captures the instability mechanism at finite density via frustration-induced magnon band deformation.

FOS: Physical sciences↗

Bayesian calibration and uncertainty quantification of a rate-dependent cohesive zone model for polymer interfaces

In this work we present a rate-dependent cohesive zone model for the fracture of polymeric interfaces and performs a Bayesian calibration, an uncertainty quantification, and a sensitivity analysis for the model. The proposed cohesive zone model accounts for both reversible elastic and irreversible rate-dependent separation sliding deformation at the interface. The viscous dissipation due to the irreversible opening at the interface is modeled using elastic-viscoplastic kinematics that incorporates the effects of strain rate. Inverse calibration of parameters for such complex models through trial and error is challenging due to the large number of parameters of the model. Moreover, the calibrated parameter values are often non-unique and uncertain when the available experimental data is limited. To tackle this challenge, we employ a Bayesian calibration approach to identify parameters from experimental data, the resulting parameters significantly enhance the accuracy of the model. To quantify the uncertainty associated with the inverse parameter estimation, a modular Bayesian approach is employed to calibrate the unknown model parameters, accounting for the parameter uncertainty of the cohesive zone model. The advantages of the Bayesian calibration over a deterministic parameter fit are demonstrated. Further, to quantify the model uncertainties, such as incorrect assumptions or missing physics, a discrepancy function is introduced, which significantly improves the model’s prediction. Finally, the total uncertainty of the model is quantified in a predictive setting. A sensitivity analysis is performed to assess how changes in the input variables of the model affect the peak load, facilitating the identification of a concise set of highly influential parameters. The present approach can be used for calibration and uncertainty quantification for other complex computational mechanics models. It should also facilitate the designing of interface materials under uncertainty.

42 ENGINEERING↗

Inexpensive and durable aerogel-based VIP cores

The goal of this project was development of low-cost aerogels to be used as cores of Vacuum Insulated Panels (VIP). The specific aims were: 1. Aerogels to be based on phenolic chemistry to minimize flammability. 2. Aerogels to be in monolithic form and to have mechanical properties sufficient to allow their use as cores of VIPs without collapsing after evacuation. 3. Aerogels to have a cost per kg lower than the cost of fumed silica, one of the most common VIP cores. The achievements are: 1. Phenolic aerogels have been fabricated in monolithic form with thermal conductivity of 0.023 W/m·K, density ~ 0.25 g/cm 3 and a modulus of compression > 10 MPa. The aerogels can withstand the stresses of VIP evacuation without any appreciable deformation. 2. Drying of aerogels was carried in the initial stages of the project via sublimation of frozen solvents, following the procedure described in M. F. Bertino and T. Selden, “Fabrication of Aerogels and Aerogel Composites by Ambient Pressure Sublimation of Frozen Solvents”, PCT/US20/39485. Monoliths as large as 30 x 30 x 2 cm can be fabricated with the proprietary ambient fabrication technique which are free of cracks and warping. 3. Cost analysis was carried out and refined multiple times, cost drivers were identified, and the fabrication procedure was streamlined. Our cost model yields an aerogel cost of $\$$5.78/kg, which compares well with the price of fumed silica ($\$$6.2/kg FOB New York as of March 2023). 4. The monoliths can be cut into custom shapes and used as VIP cores. Cores fabricated with our technique have a thermal conductivity λ = 0.011 W/m·K at a pressure >10 mbar. 5. A variant of the technology yielded fireproof materials, described in M. F. Bertino, T. Moon, G. Waller, J. Ko and D. Clifford, “Fireproof thermal insulation”, Provisional Patent Application 63/415,386. 6. A spin-off company was created (ThermaGel Innovations, Inc.) which licensed technologies developed under this award. PI Bertino is a board member of the newco which is now raising capital to build a pilot plant.

36 MATERIALS SCIENCE↗

Airfoil Computational Fluid Dynamics - 9k shapes, 2 AoA's

This dataset contains aerodynamic quantities - including flow field values (momentum, energy, and vorticity) and summary values (coefficients of lift, drag, and momentum) - for 8,996 airfoil shapes, computed using the HAM2D CFD (computational fluid dynamics) model. The airfoil shapes were designed using the separable shape tensor parameterization that encodes two-dimensional shapes as elements of the Grassmann manifold. This data-driven approach learns two independent spaces of parameter from a collection of sample airfoils. The first captures large-scale, linear perturbations, and the second defines small-scale, higher-order perturbations. For this data, we used the G2Aero database of over 19,000 airfoil shapes to learn a parameter space that captured a wide array of shape characteristics. We fixed the linear deformations to be the mean over the database and sampled new shapes over a four-dimensional parameter space of higher-order perturbation. This sampling approaches allows for isolated analysis of non-linear airfoil shape deformations while holding other aspects (e.g., airfoil thickness) approximately constant. The aerodynamic quantities for the generated airfoil were obtained using the HAM2D code, which is a finite-volume Reynolds-averaged Navier-Stokes (RANS) flow solver. We employ a fifth-order WENO scheme for spatial reconstruction with Roe's flux difference scheme for inviscid flux and second-order central differencing for viscous flux. A preconditioned GMRES method is applied for implicit integration. The Spalart-Allmaras 1-eq turbulence model is used for the turbulence closure, and the Medida-Baeder 2-eq transition model is applied to account for the effects of laminar turbulent transition. The airfoil grid is generated with a total of 400 points on the airfoil surface, the initial wall-normal spacing of y+ = 1, and an outer boundary located at 300 chord lengths away from the wall. The CFD simulations are performed at a freestream Mach number of 0.1, Reynolds number of 9M, and at two angles of attack, 4 deg. and 12 deg. The simulations were performed using the Bridges-2 system at the Pittsburgh Supercomputing Center in February 2023 as part of the INTEGRATE project funded by the Advanced Research Projects Agency - Energy in the U.S. Department of Energy. The data was collected, reformatted, and preprocessed for this OEDI submission in July 2023 under the Foundational AI for Wind Energy project funded by the U.S. Department of Energy Wind Energy Technologies Office. This dataset is intended to serve as a benchmark against which new artificial intelligence (AI) or machine learning (ML) tools may be tested. Baseline AI/ML methods for analyzing this dataset have been implemented, and a link to their repository containing those models has been provided. The .h5 data file structure can be found in the GitHub Repository resource under explore_airfoil_9k_data.ipynb.

9k↗

Calibration of elastoplastic constitutive model parameters from full-field data with automatic differentiation-based sensitivities

Here, we present a framework for calibration of parameters in elastoplastic constitutive models that is based on the use of automatic differentiation (AD). The model calibration problem is posed as a partial differential equation-constrained optimization problem where a finite element (FE) model of the coupled equilibrium equation and constitutive model evolution equations serves as the constraint. The objective function quantifies the mismatch between the displacement predicted by the FE model and full-field digital image correlation data, and the optimization problem is solved using gradient-based optimization algorithms. Forward and adjoint sensitivities are used to compute the gradient at considerably less cost than its calculation from finite difference approximations. Through the use of AD, we need only to write the constraints in terms of AD objects, where all of the derivatives required for the forward and inverse problems are obtained by appropriately seeding and evaluating these quantities. We present three numerical examples that verify the correctness of the gradient, demonstrate the AD approach's parallel computation capabilities via application to a large-scale FE model, and highlight the formulation's ease of extensibility to other classes of constitutive models.

42 ENGINEERING↗

Strong yet ductile nanolamellar high-entropy alloys by additive manufacturing

Additive manufacturing produces net-shaped components layer by layer for engineering applications. The additive manufacture of metal alloys by laser powder bed fusion (L-PBF) involves large temperature gradients and rapid cooling, which enables microstructural refinement at the nanoscale to achieve high strength. However, high-strength nanostructured alloys produced by laser additive manufacturing often have limited ductility. In this work, we use L-PBF to print dual-phase nanolamellar high-entropy alloys (HEAs) of AlCoCrFeNi 2.1 that exhibit a combination of a high yield strength of about 1.3 gigapascals and a large uniform elongation of about 14 percent, which surpasses those of other state-of-the-art additively manufactured metal alloys. The high yield strength stems from the strong strengthening effects of the dual-phase structures that consist of alternating face-centred cubic and body-centred cubic nanolamellae; the body-centred cubic nanolamellae exhibit higher strengths and higher hardening rates than the face-centred cubic nanolamellae. The large tensile ductility arises owing to the high work-hardening capability of the as-printed hierarchical microstructures in the form of dual-phase nanolamellae embedded in microscale eutectic colonies, which have nearly random orientations to promote isotropic mechanical properties. The mechanistic insights into the deformation behaviour of additively manufactured HEAs have broad implications for the development of hierarchical, dual- and multi-phase, nanostructured alloys with exceptional mechanical properties.

36 MATERIALS SCIENCE↗

Calibration of energy density functionals with deformed nuclei

Nuclear density functional theory is the prevalent theoretical framework for accurately describing nuclear properties at the scale of the entire chart of nuclides. Given an energy functional and a many-body scheme (e.g., single- or multireference level), the predictive power of the theory depends strongly on how the parameters of the energy functionals have been calibrated with experimental data. Expanded algorithms and computing power have enabled recent optimization protocols to include data in deformed nuclei in order to optimize the coupling constants of the energy functional. The primary motivation of this work is to test the robustness of such protocols with respect to some of the technical and numerical details of the underlying calculations, especially when the calibration explores a large parameter space. To this end, we quantify the effect of these uncertainties on both the optimization and statistical emulation of composite objective functions. We also emphasize that Bayesian calibration can provide better estimates of the theoretical errors used to define objective functions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Anisotropic neutron star crust, solar system mountains, and gravitational waves

"Mountains" or non-axisymmetric deformations of rotating neutron stars (NS) efficiently radiate gravitational waves (GW). We consider analogies between NS mountains and surface features of solar system bodies. Both NS and moons such as Europa or Enceladus have thin crusts over deep oceans while Mercury has a thin crust over a large metallic core. Thin sheets may wrinkle in universal ways. Europa has linear features, Enceladus has "Tiger" stripes, and Mercury has lobate scarps. NS may have analogous features. The innermost inner core of the Earth is anisotropic with a shear modulus that depends on direction. If NS crust material is also anisotropic this will produce an ellipticity, when the crust is stressed, that grows with spin frequency. This yields a braking index (log derivative of spin down rate assuming only GW spin down) very different from n=5 and could explain the maximum spin observed for neutron stars and a possible minimum ellipticity of millisecond pulsars.

79 ASTRONOMY AND ASTROPHYSICS↗

Chain rigidity controlled aggregation ability and solid-state microstructures for efficient stretchable conjugated polymer films

Stretchable conjugated polymer films with good electrical performance under mechanical deformation are highly desirable for soft electronics. However, the mechanical and electrical properties of these films, particularly in conjugated polymer:elastomer blends, are not fully understood at molecular level. Here, this study explores the relationships among molecular structure, aggregation ability, film microstructure, and the electrical/mechanical properties of three diketopyrrolopyrrole-based conjugated polymers (P1, P2, P3) with decreasing backbone rigidity and their corresponding polymer:elastomer blends. The most flexible polymer P3 shows strong aggregation, which forms highly crystalline fibers to produce fragile neat film and produces large isolated crystallites restricting charge transport in blend film. As chain rigidity increases, the P1 and P2 polymers show weaker aggregation, and produce smaller crystallites in neat films with enhanced ductility. P1 and P2 based blend films display nanocrystallites polymer networks with dispersed elastomer domains. As a result, we achieved near-constant charge mobility before and after stretching under 50 % strain for P2-based blend films with well-controlled pathways for both charge transport and energy dissipation. This study demonstrates the critical role of backbone rigidity in regulating the properties of stretchable conjugated polymer films, paving the way for more reliable and deformable materials in soft electronics.

36 MATERIALS SCIENCE↗

Uplift and Seismicity Driven by Magmatic Inflation at Sierra Negra Volcano, Galápagos Islands

Abstract Although episodes of surface uplift and elevated seismicity precede many volcanic eruptions, their temporal evolution is often complex, and apparently in contradiction to simple trends predicted by mechanical deformation models. Here, we use continuous global positioning system and seismic data recorded at Sierra Negra volcano, Galápagos Islands, to show how the edifice responded to stress changes driven by magma accumulation in a shallow sill. The rate of uplift varied during the 13 years and 6.5 m of inflation before the 2018 eruption. The number of earthquakes per unit of uplift increased exponentially with total uplift as the differential stress increased. Accordingly, the temporal seismicity rate varied in time as a function of both the total uplift and the uplift rate. The Gutenberg‐Richter b ‐value decreased as a function of total uplift. In the final six months before the eruption, a sequence of large ( M > 4) earthquakes regulated the state of stress on the fault, each being followed by 2–3 days of postseismic quiescence, and retarding the increase in seismicity rate. These earthquakes did not affect the overall uplift rate. Subsidence of 8.5 m accompanied the 2‐month eruption. On resumption of uplift, the number of earthquakes per unit of uplift was very low, and the b ‐value high, reflecting the relaxed stress state of the fault system. These observations show that crustal deformation becomes increasingly brittle at higher stress states, and supports theoretical models based on elastic‐brittle mechanics. They suggest that joint interpretation of deformation and seismicity is key for forecasting future eruptions in similar volcanic settings.

Bell, Andrew Forbes↗

Sea Ice Rheology Experiment (SIREx): 2. Evaluating Linear Kinematic Features in High-Resolution Sea Ice Simulations

Simulating sea ice drift and deformation in the Arctic Ocean is still a challenge because of the multiscale interaction of sea ice floes that compose the Arctic Sea ice cover. The Sea Ice Rheology Experiment (SIREx) is a model intercomparison project of the Forum of Arctic Modeling and Observational Synthesis (FAMOS). In SIREx, skill metrics are designed to evaluate different recently suggested approaches for modeling linear kinematic features (LKFs) to provide guidance for modeling small-scale deformation. These LKFs are narrow bands of localized deformation that can be observed in satellite images and also form in high resolution sea ice simulations. In this contribution, spatial and temporal properties of LKFs are assessed in 36 simulations of state-of-the-art sea ice models and compared to deformation features derived from the RADARSAT Geophysical Processor System. All simulations produce LKFs, but only very few models realistically simulate at least some statistics of LKF properties such as densities, lengths, or growth rates. All SIREx models overestimate the angle of fracture between conjugate pairs of LKFs and LKF lifetimes pointing to inaccurate model physics. The temporal and spatial resolution of a simulation and the spatial resolution of atmospheric boundary condition affect simulated LKFs as much as the model's sea ice rheology and numerics. Only in very high resolution simulations (≤2 km) the concentration and thickness anomalies along LKFs are large enough to affect air-ice-ocean interaction processes.

54 ENVIRONMENTAL SCIENCES↗

On unitarity of the hypergeometric amplitude

The hypergeometric amplitude is a one-parameter deformation of the Veneziano amplitude for four-point tachyon scattering in bosonic string theory that is consistent with S-matrix bootstrap constraints. In this article we construct a similar hypergeometric generalization of the Veneziano amplitude for type-I superstring theory. We then rule out a large region of the (r, m 2 , D) parameter space as non-unitary, and establish another large subset of the (r, m 2 , D) parameter space where all of the residue’s partial wave coefficients are positive. We also analyze positivity in various limits and special cases. As a corollary to our analysis, we are able to directly demonstrate positivity of a wider set of Veneziano amplitude partial wave coefficients than what has been presented elsewhere.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

“Self-trapping” in solar cell hybrid inorganic-organic perovskite absorbers

In the simplest picture, a “self-trapped” polaron forms when an excess electron or hole deforms a crystal lattice, creating a potential well with bound states. Properties of self-trapped polarons in methylammonium lead iodide perovskite (MAPbI 3 ), which is widely used as solar cell absorber, are of great interest, and are a subject of ongoing investigations and debates concerning the existence of large polarons with the co-presence of metastable self-trapping. Herein, we employ a self-interaction-free density functional theory method to investigate the stability of small polarons in tetragonal MAPbI 3 phase. The electron small polaron is found to be unstable, while the hole small polaron is found to be metastable at realistic operation temperatures of solar cells. Further, the hole polaron is found to have a hole band close to the conduction band, which in conjunction with its metastability suggests that small polarons will have an appreciable effect on charge-carrier recombinations in MAPbI 3 . Further, in this study, we posit that the existence of the metastable polarons in addition to the large polarons may explain the experimentally observed non-monotonic temperature dependence of bimolecular charge-carrier recombination rate in tetragonal MAPbI 3 phase.

14 SOLAR ENERGY↗

The influence of temperature on the strain-hardening behavior of Fe-22/25/28Mn-3Al-3Si TRIP/TWIP steels

In this work, the influence of temperature and stacking fault energy (SFE) on the strain-hardening behavior and critical resolved shear stress for twinning was investigated for three Fe–22/25/28Mn–3Al–3Si wt.% transformation- and twinning-induced plasticity (TRIP/TWIP) steels. The SFEs were calculated by two different methods, density functional theory and statistical thermodynamic modeling. The dislocation structure, observed at low levels of plastic deformation, transitions from “planar” to “wavy” dislocation glide with an increase in temperature, Mn content, and/or SFE. The change in dislocation glide mechanisms from planar to wavy reduces the strain hardening rate, in part due to fewer planar obstacles and greater cross slip activity. Additionally, the alloys exhibit a large decrease in strength and ductility with increasing temperature from 25 to 200 °C, attributed to a substantial reduction in the thermally activated component of the flow stress, predominate suppression of TRIP and TWIP, and a significant increase in the critical resolved shear stress for mechanical twinning. Interestingly, the increase in SFE with temperature had a rather minor influence on the critical resolved shear stress for mechanical twinning, and other temperature dependent factors which likely play a more dominant role are discussed.

36 MATERIALS SCIENCE↗

Renormalization of Ising cage-net model and generalized foliation

A large class of type-I fracton models, including the X-cube model, have been found to be fixed points of the foliated renormalization group (RG). The system size of such foliated models can be changed by adding or removing decoupled layers of 2D topological states and continuous deformation of the Hamiltonian. In this paper, we study a closely related model—the Ising cage-net model—and find that this model is not foliated in the same sense. In fact, we point out certain unnatural restrictions in the foliated RG, and find that removing these restrictions leads to a generalized foliated RG under which the Ising cage-net model is a fixed point, and which includes the original foliated RG as a special case. The Ising cage-net model thus gives a prototypical example of the generalized foliated RG, and its system size can be changed either by condensing/uncondensing bosonic planon excitations near a 2D plane or through a linear-depth quantum circuit in the same plane. Additionally, we show that these two apparently different RG procedures are closely related, as they lead to the same gapped boundary when implemented in part of a plane. Finally, we briefly discuss the implications for foliated fracton phases, whose universal properties will need to be reexamined in light of the generalized foliated RG.

2-dimensional systems↗